ch01 JWBK035-Vince February 22, 2007 21 : 43 Char Count= 0
The Random Process and Gambling Theory 25tails again, extendingthe streak to two events.Thereis also a 50% chance
itwill come up heads, endingthe streak at one.Goinginto the third flipwe
face the same possibilities.Continuingwith thislogic we can construct the
followingtable, assumingwe aregoingto flipacoin 1,024 times:Length of StreakNo. of Streaks
OccurringHow Often
Compared to
Streak of One Probability1 512 1 .50
2 256 1/2 .25
3 128 1/4 .125
4 64 1/8 .0625
5 32 1/16 .03125
6 16 1/32 .015625
7 8 1/64 .0078125
8 4 1/128 .00390625
9 2 1/256 .001953125
10 1 1/512 .0009765625
11 + 1 1/1024 .00048828125The real pattern does not end at thispoint;ratherit continues with
smaller and smaller numbers.
Remember that thisis the expected pattern.The real-life pattern,
should yougo out and record 1,024 coinflips, will resemble this, but most
likelyit won’t resemble this exactly.This pattern of 1,024 coin tossesis for
afair 50/50game.In agame where the house has the edge, you can expect
the streaks to be skewed by the amount of the house advantage.Determining Dependency
As we have already explained, the coin tossisanindependent trials pro-
cess.This can be deduced byinspection,in that we can calculate the exact
probability statement prior to each toss anditis always the same from
one toss to the next.There are other events, such as blackjack, that are
dependent trials processes.These, too, can be deduced byinspection,in
that we can calculate the exact probability statement prior to each draw of
a card, anditis not always the same from one draw to the next.For still
other events, dependence on prior outcomes cannot be determined upon
inspection.Such an eventis the profit and loss stream of tradesgenerated
by a tradingsystem.For these types of problems we need more tools.